This paper examines the conundrum faced when one attempts to understand the dynamics of black hole formation and evaporation without abandoning unitary evolution. Previous efforts to resolve this puzzle assume that information escapes in corrections to the Hawking process, that an arbitrarily large amount of information is transmitted by a Planckian energy or contained in a Planck-sized remnant, or that the information is lost to another universe. Each of these possibilities has serious difficulties. This paper considers another alternative: remnants that carry large amounts of information and whose size and mass depend on their information content. The existence of such objects is suggested by attempts to incorporate a Planck-scale cutoff into physics. They would greatly alter the late stages of the evaporation process. The main drawback of this scenario is the apparent noncausal behavior behind the horizon.